In general, exothermal reaction for obtaining a product (B) from a starting compound (A) is easy to abruptly generate heat if the reaction is carried out at a temperature exceeding a prescribed reaction temperature and therefore, it is required to carry out the reaction while efficiently removing heat. As a reactor for carrying out such reaction, a heat exchange reactor (1′) which is provided with a reaction tube (2) and a reactor shell (3) covering the surrounding of the reaction tube (2) as shown in FIG. 3 has been widely used. With the reactor (1′), the product (B) is obtained by exothermal reaction while passing the starting compound (A) in the reaction tube (2). The reactor shell (3) is divided into a plurality of regions (31 to 34) along the passing direction of the starting compound (A) and each of the separate regions (31 to 34) is filled with a heat medium (C1 to C4) to carry out heat exchange between the inside of the reaction tube (2) and the respective heat media (C1 to C4) [reference to JP-A-2001-129384]. The heat exchange reactor (1′) is capable of efficiently removing heat and keeping the temperature in the reaction tube (2) at a prescribed reaction temperature by changing the temperature of the respective heat media (C1 to C4) in accordance with the heat generation quantities of the respective regions (31 to 34).